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JOHN A. FRONIMOS ET AL.


concave element. Grammont (1979) was inspired to invent this procedure by the evolutionary transition of human ancestors from quadrupedalism to bipedalism. As described by Baulot et al. (2011: p. 2426), “the freeing of the human upper limb resulted in a functional reversal of the roles of the humerus and the glenoid.” In humans, the hand is not involved in weight support and represents the free end of the forelimb under most conditions. The results of the present analysis suggest that a reverse shoulder joint should be capable of greater rotational stability than the normal anatomical orientation in humans. Conversely, it is expected that a comparable reversal applied to the human femoro-acetabular joint, if such a prosthesis existed, would have a destabilizing influence.


Conclusions The functional significance of concavo-convex


joint polarity has been a source of lingering uncertainty, including with regard to opistho- coelous and procoelous vertebrae. Physical modeling of concavo-convex joints reveals that proximally concave joints are significantly more resistant to joint failure. The strongly conserved pattern of cervical opisthocoely and caudal procoely in sauropod dinosaurs is, therefore, best explained as providing greater passive stabilization of the intervertebral joints than the opposite polarity. The sauropod configuration also would have permitted greater mobility, mechanical advantage of the supporting ligaments and muscles, and distal loading (i.e., a longer neck or tail) without sacrificing stability. The universal condition of cervical opisthocoely in sauropods may have been necessary for the evolution of large body size and neck hyperelongation. Among vertebrates, exceptions to the sauropod-type patternmay be dependent on limited mobility, short neckswith large, heavy heads, or energetically costly muscular activity for stabilization. Cervical procoely and caudal opisthocoely could be advantageous if the loading direction of the intervertebral joints was reversed, as during the adoption of a tripodal stance or, perhaps, during particular forms of locomotion. Further research into the loading regimes of intervertebral joints during these behaviors is needed. The concept


that concavo-convex joint polarity reflects particular loading regimes provides an explana- tion for some patterns of polarity in the appendicular skeleton, as in the case of the tetrapod glenohumeral and femoro-acetabular joints, and may offer new insights into the functional evolution of these joints.


Acknowledgments We wish to thank S. O’Grady and


S. O’Malley of the University of Michigan 3D Lab for their help with the design and printing of the models used in this study. W. Sanders provided advice and assistance with material selection and molding and casting. M. Cherney and T. Hudgins aided greatly in the design and construction of the experimental testing rigs. A. Rountrey provided access to equipment and space for conducting experiments. We are grateful to C. Abraczinskas for guidance on the execution of the figures. Access to the sauropod specimens pictured in Figure 1 was provided by D. Campos, R. Machado, and I. Yamamoto (Museu de Ciências da Terra). The color scheme in Figure 7 was developed using ColorBrewer, Version 2.0. We thank the University of Michigan Library’s Buhr Remote Shelving Facility staff for providing high-quality scans of Fick (1890); nineteenth- century literature was also provided by the HathiTrust Digital Library and the Biodiver- sity Heritage Library. Vielen Dank to J. Fahlke for input on German translations; the transla- tion of Janensch (1950) was provided through the Polyglot Paleontologist website (http:// www.paleoglot.org) courtesy of G. Maier. We thank editor C. Jaramillo and two anonymous reviewers for their helpful feedback on this manuscript. This study represents part of the dissertation of J.A.F., and the authors thank committee members D. Fisher, P. Gingerich, and L. MacLatchy for their input throughout. This project benefited from discussions with University of Michigan Museum of Paleontology graduate students M. Cherney, J. El Adli, L. Joel, K. Loughney, E. Moacdieh, K. Purens, T. Smiley, V. Syverson, and M. Veitch, and many others in the Department of Earth and Environmental Sciences. Funding was provided by the University of Michigan


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